Complex Chebyshev approximation to stable IIR filters design

Sugita, Tomomi; Aikawa, Naoyuki

doi:10.1109/pacrim.2001.953695

Cited by 3 publications

(2 citation statements)

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“…In this example, we designed a filter with the same specifications as the low-pass filter obtained by successive projection based on Rouché's theorem [4]. The design conditions were M = 6, N = 12, τ d = 9, ω p = 0.5π, ω s = 0.6π; the low-pass filter had a weight of 1 across the entire band.…”

Section: Design Examplementioning

confidence: 99%

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Optimal design of IIR filters using linear semi‐indefinite programming method

Yamazaki

Suyama

2011

Elect Comm in Japan

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SUMMARYAn optimal design method for stable IIR (Infinite Impulse Response) filters under the min-max criterion is proposed. The design problem considered is the complex Chebyshev approximation of a rational function including the stability constraint. We formulate this problem as a problem of real linear semi-infinite programming problem using the real rotation theorem. The problem is solved by the three-phase method; one of the methods is used for solving semi-infinite programming problems. The threephase method includes three operations. In the first operation, some active constraint candidates are selected by the iterative simplex method. Next, the second operation integrates some degenerate constraints. In the third operation, the approximate solution obtained up to the second operation is adjusted so as to satisfy the optimality condition. The filters designed by the method are found to be more precise than those designed by the conventional method. Several design examples are presented to demonstrate the effectiveness of the proposed method.

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Section: Design Examplementioning

confidence: 99%

“…On the other hand, there are design methods with regard for stability, such as a method using successive projection based on Rouché's theorem [4], a method based on semidefinite programming [5], and a quadratic programming method using real positiveness as a constraint to assure stability [6].…”

Section: Introductionmentioning

confidence: 99%